Fig. 1: Pre- and post-outage NBLE results aligned with the NAWI blackout’s key events. | Nature Communications

Fig. 1: Pre- and post-outage NBLE results aligned with the NAWI blackout’s key events.

From: Quantifying local stability and noise levels from time series in the US Western Interconnection blackout on 10th August 1996

Fig. 1

The results are robust to variations in window size (cf. SI S16). Dark- and light-green shadings represent 16% to 84% and 1% to 99% percentile credibility bands, respectively. Shaded time intervals refer to the listed events. a Timeline (in PDT) and power grid islands61. BPA denotes Bonneville Power Administration. b Detrended pre-outage bus voltage frequency \({\tilde{\omega }}_{{\rm{P}}}(t)\). The data oscillations at  ~ 0.2 Hz to 0.4 Hz (cf. inset) are not captured by the NBLE drift (cf. SI S3, S8, and S15). c Following the 500 kV Keeler-Allston line trip, a turbulent period of control actions and destabilising events is reflected by pronounced fluctuations around drift slope \({\hat{\zeta }}_{{\rm{NBLE}}}\approx -3.3\). Estimates increase sharply with the loss of the McNary power units, exhibiting a smoother trend toward the islanding process, consistent with the concepts in Supplementary Box S1, as grid component failures affect the frequency drift rather than noise levels. d Noise levels \(\hat{\Psi }\) increase sharply about 2 min before the 500 kV Keeler-Allston line trip, indicating greater impact of fast-scale phenomena, possibly due to the tree-related high-impedance fault (THIF) or a sudden load imbalance (cf. SI S17). e Detrended bus voltage frequency \({\tilde{\omega }}_{{\rm{R}}}(t)\) during restoration. The black-hatched interval’s end coincides with the end of \({\tilde{\omega }}_{{\rm{P}}}(t)\). f Initial drift slopes \({\hat{\zeta }}_{{\rm{NBLE}}}\gtrsim 0\) are unreliable, as the windows include pre-outage data. The barely stable grid state during the orange-shaded key restoration interval is reasonable, as most of the grid components are recovered only stepwise throughout this period, with some not restored until much later, on 16th August 1996. The system steadily approaches the physical pre-outage configuration, including lines, power units, and loads, reflected by drift slopes reaching a stable plateau during the green-shaded period. Nine windows exhibit spiking credible intervals due to outliers. g Initial noise levels \(\hat{\Psi }\) are unreliable (cf. f). The steepening potential during restoration lowers the noise levels as the system stabilises in the operational fixed point (cf. Supplementary Box S1b). f, g Grey lines show outlier (orange in insets) effects, causing a bias of roughly one window length (cf. Methods; SI S18).

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